Question

How to determine the average rate of change with an interval

Answer 1

b) Δf/Δx = 22.5

Explanation:

To determine the average rate of change, we use the following formula:

`\begin{gathered} r=(\Delta f)/(\Delta x) \\ \\ (\Delta f)/(\Delta x)=(f(b)-(f(a))/(b-a) \end{gathered}`

We substitute in each case and get the following:

`\begin{gathered} (\Delta f)/(\Delta x)=(3\cdot\left(2\right)^(2\cdot2)-3\cdot\left(2\right)^(2\cdot\:0))/(2-0) \\ \\ (\Delta f)/(\Delta x)=(3\cdot2^4-3\cdot2^0)/(2) \\ \\ (\Delta f)/(\Delta x)=(3\cdot16-3)/(2)=(48-3)/(2)=(45)/(2) \\ \\ (\Delta f)/(\Delta x)=22.5 \end{gathered}`

Therefore, the correct answer is b) Δf/Δx = 22.5